Characterization of plastically compressible solids via spherical indentation

The response in spherical indentation is used to identify material properties for plastically compressible materials with presumed known elastic properties. The materials are assumed to be characterized by a Deshpande–Fleck constitutive relation (Deshpande and Fleck, 2000). The indentation force versus indentation depth responses and the residual surface profiles (the surface profiles after unloading) are calculated for two sets of material parameters. These are regarded as the “experimental” input materials. The constitutive parameters for these two materials are identified using the Bayesian-type statistical approach of Zhang et al. (2019) both for noise-free and for noise-contaminated data. The uniaxial stress–strain responses obtained from the spherical indentation responses are good approximations of those of the “experimental” input materials, particularly if surface profile data is used, but the quality of the approximation decreases with increasing noise amplitude. Plastic compressibility is found to have a relatively small effect on the correction factor β in the Oliver–Pharr relation (Oliver and Pharr, 2004) between the unloading slope and the effective (or reduced) elastic modulus. The indentation response of the plastically compressible materials can be well-represented by a nearly incompressible plastic constitutive relation but the inferred uniaxial stress–strain response is a poor representation of the “experimental” material uniaxial stress–strain response. The predicted residual surface profile is less dependent on the assumed elastic constant values than is the indentation force versus indentation depth response. The indentation force versus indentation depth responses in spherical indentation for three materials with very different uniaxial stress–strain curves are found to be indistinguishable if the indentation depth is sufficiently small but are distinguishable if the indentation depth is sufficiently large.